Charges and Energy in Chern-Simons Theories and Lovelock Gravity
G. Allemandi, M. Francaviglia, M. Raiteri
TL;DR
This paper derives a simple covariant expression for conserved charge variations in Lovelock and Lovelock-Maxwell gravities, extending Chern-Simons theory concepts to higher dimensions and black hole entropy calculations.
Contribution
It provides a unified, covariant formalism for calculating conserved quantities in Lovelock gravity, simplifying complex Lagrangian variations and recovering black hole entropy expressions.
Findings
Derived a simple expression for charge variations in Lovelock gravity.
Validated the formalism with specific applications to black hole entropy.
Extended the covariant formalism to Lovelock-Maxwell gravity.
Abstract
Starting from the SO(2,2n) Chern-Simons form in (2n+1) dimensions we calculate the variation of conserved quantities in Lovelock gravity and Lovelock-Maxwell gravity through the covariant formalism developed in gr-qc/0305047. Despite the technical complexity of the Lovelock Lagrangian we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance of the theory. The viability of the result is tested in specific applications and the formal expression for the entropy of Lovelock black holes is recovered.
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